Multi-Dimensional Scaling (MDS) Algorithm Implementation

This implementation provides comprehensive functionality for Multi-Dimensional Scaling (MDS), a powerful data analysis technique widely used for feature extraction, feature selection, and dimensionality reduction of matrices. MDS serves as an essential tool for analyzing and visualizing high-dimensional data by transforming complex datasets into lower-dimensional representations while preserving intrinsic data relationships. The algorithm operates by computing pairwise distance matrices between data points and reconstructing these relationships in a reduced-dimensional space (typically 2D or 3D). Key implementation components include distance matrix calculation using Euclidean or custom distance metrics, eigenvalue decomposition for stress minimization, and coordinate transformation through classical scaling approaches. The code handles both metric MDS for quantitative distance preservation and non-metric MDS for ordinal data relationships. This technique finds extensive applications across multiple domains including data mining, machine learning pipeline development, market research analytics, and biological data visualization. The implementation includes optimization for handling large datasets through efficient matrix operations and provides visualization capabilities for result interpretation.